📚 Year 7 AQA Geography: Quick-Reference Handbook of Formulas and Theorems | Year 7 AQA 地理：公式定理速查手册
This quick-reference handbook provides AQA Year 7 geography students with essential formulas and key geographical theorems needed for map skills, population studies and physical geography. Use it to revise how to calculate distances, areas, gradients, population density, river velocity and more. Each formula is clearly stated with a practical example or explanation.
本速查手册为 AQA Year 7 地理学生提供地图技能、人口研究和自然地理所需的关键公式与重要地理定理。可用于复习距离、面积、坡度、人口密度、河流流速等的计算方法。每个公式均配有清晰表述和实用说明。
1. Map Scale and Distance | 比例尺与距离
Map scale expresses how much the real world has been reduced to fit on a map. Three common types are: ratio scale (1:50,000), verbal scale (“1 cm to 0.5 km”) and a linear scale bar.
比例尺表示真实世界被缩小以适合地图的程度。三种常见类型：比数比例尺（1:50,000）、文字比例尺（”1 cm 代表 0.5 km”）和线段比例尺。
The fundamental formula converts map distance to real-world distance:
Real Distance = Map Distance × Scale Denominator
基础公式将地图距离转换为实际距离：
实际距离 = 地图距离 × 比例尺分母
For a 1:25,000 map, 4 cm on the map equals 4 × 25,000 = 100,000 cm, which is 1,000 m or 1 km.
对于 1:25,000 地图，地图上 4 cm = 4 × 25,000 = 100,000 cm，即 1,000 m 或 1 km。
Always convert units carefully. Use the metric ladder: 1 km = 1,000 m = 100,000 cm. Divide by 100 to go from cm to m, and by 100,000 to go from cm to km.
务必仔细换算单位。使用公制阶梯：1 km = 1,000 m = 100,000 cm。从厘米转米除以100，转公里除以100,000。
2. Measuring Straight-Line and Curved Distances | 测量直线与曲线距离
For straight-line distances, use a ruler to measure the length on the map in centimetres, then apply the scale formula. Always measure from the centre of one symbol to the centre of another.
直线距离用直尺量出地图上的厘米长度，再应用比例尺公式。始终从图例符号的中心量到另一个符号的中心。
For curved distances, such as a winding river or road, use the string-and-mark method. Lay a piece of string along the curve, mark the end point, then straighten the string against a ruler to find the map distance.
测量曲线距离（如蜿蜒的河流或道路），使用棉线描记法。将棉线沿曲线放置，标出终点，然后将棉线拉直，用直尺量出地图距离。
Once you have the map distance in cm, convert it to real distance using:
Real Distance (m) = Map Distance (cm) × Scale Denominator ÷ 100
获得以厘米计的地图距离后，用它来换算实际距离：
实际距离 (m) = 地图距离 (cm) × 比例尺分母 ÷ 100
3. Converting Map Area to Real Area | 地图面积转换为实际面积
When converting an area measured on a map to the real-world area, remember that area scales by the square of the scale factor. The formula is:
Real Area = Map Area × (Scale Denominator)²
将地图上量得的面积转换为实际面积时，须牢记面积按比例尺因子的平方进行缩放。公式为：
实际面积 = 地图面积 × (比例尺分母)²
Example: on a 1:50,000 map, 1 cm² represents 1 × (50,000)² = 2,500,000,000 cm². Convert to m² by dividing by 10,000 (since 1 m² = 10,000 cm²), giving 250,000 m². To express in km², divide by 1,000,000, which gives 0.25 km².
示例：在 1:50,000 地图上，1 cm² 代表 1 × (50,000)² = 2,500,000,000 cm²。除以10,000 转换为平方米（因为 1 m² = 10,000 cm²），得 250,000 m²。再除以 1,000,000 得到 0.25 km²。
A quick way: for a 1:50,000 map, 1 cm² on the map equals 0.25 km² on the ground. Learn the square relationship to avoid mistakes.
快速记忆法：对于 1:50,000 地图，图上 1 cm² = 实地 0.25 km²。掌握这种平方关系可避免出错。
4. Height, Spot Heights and Triangulation Pillars | 高度、标高点与三角测量站
Height on a map is given in metres above sea level (ordnance datum). A spot height is a black dot with a number showing the exact elevation at that point. A triangulation pillar is a blue triangle with a dot, often on hilltops, giving a very accurate height.
地图上的高度以海平面以上的米数表示（英国国家高程基准）。标高点是一个带有数字的黑点，显示该点的精确高程。三角测量站是一个带点的蓝色三角形，常位于山顶，给出非常准确的高度。
The theorem for relief interpretation: every point along the same contour line has the same height. Spot heights help you build an accurate picture of the landscape.
地形判读定理：同一等高线上的每一点高度相同。标高点有助于准确构建周围地形的图像。
5. Contour Lines and Contour Interval | 等高线与等高距
Contour lines are orange or brown lines connecting points of equal elevation. The contour interval is the vertical difference between adjacent contour lines, stated in the map legend (e.g. 10 m).
等高线是连接相同高程点的橙色或棕色线条。等高距是相邻等高线之间的垂直高差，在地图图例中注明（例如 10 m）。
A fundamental theorem: closely spaced contours indicate a steep slope, while widely spaced contours indicate a gentle slope. Evenly spaced contours show a uniform slope.
一条基本定理：等高线密集表示陡坡，等高线稀疏表示缓坡。等高线间距均匀则表示均匀坡。
To find the height difference between two points, count the number of contour intervals between them and multiply by the contour interval. Add or subtract from known spot heights.
求两点高度差时，数出两点间的等高线间隔数，乘以等高距。然后从已知标高点高度加上或减去该值。
6. Gradient Calculation | 坡度计算
Gradient describes the steepness of a slope. It is the ratio of vertical rise to horizontal distance. The formula is:
Gradient = Vertical Rise (height difference) ÷ Horizontal Distance
坡度描述斜坡的陡峭程度，是垂直升高与水平距离的比值。公式为：
坡度 = 垂直升高 (高差) ÷ 水平距离
Express gradient as a ratio, such as 1:20, meaning for every 1 unit of rise you move 20 units horizontally. Alternatively, use a percentage: gradient % = (rise ÷ run) × 100.
坡度可用比值表示，如 1:20，意为每上升1个单位水平移动20个单位。也可用百分比：坡度 % = (升高 ÷ 水平距离) × 100。
Example: a hillside rises 50 m over a horizontal distance of 200 m. Gradient = 50 ÷ 200 = 0.25, which is 1:4 or a 25% gradient – a very steep slope.
示例：山坡水平距离 200 m 内升高 50 m。坡度 = 50 ÷ 200 = 0.25，即 1:4 或 25% 的坡度——属于陡坡。
7. Four-Figure and Six-Figure Grid References | 四位与六位网格参考
Grid references pinpoint locations on an Ordnance Survey map. The golden rule is “along the corridor and up the stairs”: read the easting (horizontal lines) first, then the northing (vertical lines).
网格参考用于精确定位地形测量图上的位置。黄金法则是“沿走廊向前，再上楼”：先读东距（水平数字），再读北距（垂直数字）。
A four‑figure grid reference (e.g. 18,45) gives a 1 km × 1 km square. The first two digits are the easting; the last two are the northing. The reference locates the bottom‑left corner of that square.
四位网格参考（如 18,45）给出一个 1 km × 1 km 的方格。前两位是东距，后两位是北距。该参考定位方格的左下角。
For greater precision, a six‑figure grid reference (e.g. 184,457) divides each square into tenths. The extra digit in the easting tells you how many tenths across the square, and the extra northing digit tells you how many tenths up the square.
为更精确，六位网格参考（如 184,457）把每个方格十等分。额外的东距数字表示方格内横向十分之几的位置，额外的北距数字表示方格内纵向十分之几的位置。
Theorem: a six‑figure grid reference gives a location to the nearest 100 m. Always write the reference with the easting first, no punctuation between groups.
定理：六位网格参考可将位置精确到 100 m 以内。书写时始终东距在前，两组数字间不加标点。
8. Compass Directions and Bearings | 罗盘方向与方位角
A compass can be divided into 16 points (N, NNE, NE, ENE, E, etc.), but for precision bearings are measured in degrees clockwise from north, from 0° to 360°.
罗盘可分为16个方位点（北、东北偏北、东北、东北偏东、东等），但精确的方位角是按顺时针从北测量，范围为 0° 到 360°。
To find a bearing on a map, draw a line from the centre of the start point to the centre of the destination. Place a protractor with 0° aligned to grid north, and read the angle clockwise. The formula-like rule is:
Bearing = angle measured clockwise from north
在地图上求方位角，从起点中心到终点中心画线。将量角器的 0° 对准网格北，顺时针读取角度。类似公式的规则为：
方位角 = 从北顺时针测得的角度
Grid north may differ from true north and magnetic north, but for Year 7 exercises using OS maps, you can rely on grid north.
网格北可能与真北和磁北不同，但在 Year 7 使用 OS 地图的练习中，可依赖网格北。
9. Population Density | 人口密度
Population density measures how crowded a place is. The formula is straightforward:
Population Density = Total Population ÷ Land Area (km²)
人口密度衡量一个地方的拥挤程度。公式简单直接：
人口密度 = 总人口 ÷ 土地面积 (km²)
Example: a town has 12,000 people living in an area of 6 km². Density = 12,000 ÷ 6 = 2,000 people per km². High densities are often found in cities; low densities in rural areas.
示例：一镇有12,000人，面积6 km²。密度 = 12,000 ÷ 6 = 2,000 人/km²。高密度常见于城市，低密度见于乡村。
Always check that the area and population refer to the same administrative unit, and use consistent units. Convert if necessary.
务必确保面积和人口数据对应同一行政区，且单位一致。必要时进行换算。
10. River Velocity | 河流流速
River velocity is the speed at which water flows, usually measured in metres per second (m/s). The basic formula is:
Velocity = Distance ÷ Time
河流流速是水体流动的速度，通常以米每秒（m/s）为单位。基本公式为：
流速 = 距离 ÷ 时间
In fieldwork, you might use a float (e.g. an orange) and measure the time it takes to travel a known distance. The surface velocity is then corrected to mean velocity by multiplying by a factor, often 0.8 or 0.85, because friction slows water near the bed and banks.
在实地考察中，可以使用浮标（如一个橙子）并测量其漂过已知距离所用的时间。然后将表面流速乘以一个系数（常为 0.8 或 0.85）换算为平均流速，因为河床和河岸的摩擦会减慢水流。
Mean velocity theorem: mean velocity ≈ surface velocity × 0.8. This adjusts for the vertical velocity profile in a river channel.
平均流速定理：平均流速 ≈ 表面流速 × 0.8。这修正了河道中的垂向流速分布。
11. River Discharge | 河流流量
Discharge (Q) is the volume of water passing a point in a river per unit time, measured in cubic metres per second (cumecs, m³/s). It is calculated using:
Q = A × V
流量 (Q) 是单位时间内通过河流某一点的水量体积，单位为立方米每秒（m³/s）。计算公式为：
Q = A × V
Where A is the cross-sectional area of the channel (width × mean depth, measured in m²) and V is the mean velocity (m/s).
其中 A 为河道横截面积（宽度 × 平均水深，单位 m²），V 为平均流速 (m/s)。
Example: a stream has an average width of 4 m, an average depth of 0.5 m, and a mean velocity of 0.8 m/s. A = 4 × 0.5 = 2 m². Q = 2 × 0.8 = 1.6 m³/s.
示例：一条溪流平均宽度 4 m，平均水深 0.5 m，平均流速 0.8 m/s。A = 4 × 0.5 = 2 m²。Q = 2 × 0.8 = 1.6 m³/s。
Discharge theorem: in a river channel, discharge is constant along a reach, even if width and depth change, as long as no water is added or lost. This is the continuity equation.
流量定理：只要没有水量增减，河道沿程流量保持不变，即使宽度和深度变化亦然。这是连续性方程。
12. Climate Averages, Temperature Range and Precipitation Totals | 气候平均值、温度范围与降水总量
Climate graphs display monthly temperature and precipitation. Useful statistics can be derived from these data using simple formulas.
气候图表展示月均温和降水量。可用简单公式从中得出有用的统计数据。
Mean annual temperature: sum of 12 monthly mean temperatures divided by 12.
Annual Mean Temperature = Σ Monthly Temperatures ÷ 12
年平均气温：12个月均温之和除以12。
年平均气温 = Σ 月均温 ÷ 12
Temperature range: the difference between the warmest and coldest monthly mean temperatures.
Temperature Range = Max Monthly Mean – Min Monthly Mean
温度范围：最暖月均温与最冷月均温之差。
温度范围 = 最高月均温 – 最低月均温
Total annual precipitation: sum of all 12 monthly precipitation values. Precipitation is measured in millimetres (mm). Do not confuse with mean – you add them up.
Annual Precipitation = Σ Monthly Precipitation (mm)
年降水总量：12个月降水量之和。降水量以毫米（mm）为单位。不要与平均值混淆——应直接相加。
年降水量 = Σ 月降水量 (mm)
A climate theorem: large temperature ranges often indicate a continental location, while small ranges suggest maritime influence. High annual precipitation with a small range points to an equatorial climate.
气候定理：年温差大常表明大陆性位置，温差小表明海洋性影响。降水量大且温差小指向赤道气候。
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